non-linear transformation

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Hello, I'm still relatively new to Opencv. I am trying to produce what is turning out to be a rather difficult transformation.

I have a 4096x4096 black and white image. The area of interest is a circular ring which has a width of 756 pixels, making it occupy the majority of the image. What I need to do is to cut through the ring at a certain radius and stretch the image straight. stretching everything inside the ring. The end result would be an image that was 756 pixels high and 2PI( outer radius of ring).

Can this be done with an affine transformation? Or do I need to use something else.

Thanks, Dan